U.S. patent application number 10/174323 was filed with the patent office on 2003-03-20 for control method for an electromagnetic actuator for the control of a valve of an engine from an abutment condition.
Invention is credited to Padroni, Gianni.
Application Number | 20030052763 10/174323 |
Document ID | / |
Family ID | 11439435 |
Filed Date | 2003-03-20 |
United States Patent
Application |
20030052763 |
Kind Code |
A1 |
Padroni, Gianni |
March 20, 2003 |
Control method for an electromagnetic actuator for the control of a
valve of an engine from an abutment condition
Abstract
A control method for an electromagnetic actuator for the control
of a valve of an engine from an abutment condition, in which an
actuator body actuating the valve and disposed to move between two
electromagnets is maintained in abutment against a first excited
electromagnet and against the action of at least one elastic body;
in order to bring the actuator body into abutment against a second
electromagnet, the first electromagnet is de-excited and the second
electromagnet is then excited by means of excitation parameters,
which are determined as a function of the measurement of the mean
value of the disturbance force acting on the valve during the stage
of de-excitation of the first electromagnet.
Inventors: |
Padroni, Gianni;
(Portoferraio, IT) |
Correspondence
Address: |
BAKER & DANIELS
111 E. WAYNE STREET
SUITE 800
FORT WAYNE
IN
46802
|
Family ID: |
11439435 |
Appl. No.: |
10/174323 |
Filed: |
June 18, 2002 |
Current U.S.
Class: |
335/220 |
Current CPC
Class: |
H01F 7/1844 20130101;
F01L 2009/2109 20210101 |
Class at
Publication: |
335/220 |
International
Class: |
H01F 007/08 |
Foreign Application Data
Date |
Code |
Application Number |
Jun 19, 2001 |
IT |
BO2001A000390 |
Claims
1. A control method for an electromagnetic actuator (1) for the
control of a valve (2) of an engine from an abutment condition, in
which abutment condition an actuator body (4) actuating the valve
(2) and disposed to move between two electromagnets (8) is
maintained in abutment against a first excited electromagnet (8)
and against the action of at least one elastic body (9); in order
to bring the actuator body (4) into abutment against a second
electromagnet (8), the first electromagnet (8) is de-excited and
the second electromagnet (8) is subsequently excited, the method
being characterised by the measurement during the stage of
de-excitation of the first electromagnet (8) of a mean value of the
disturbance force (F.sub.d) acting on the valve (2) and by the
calculation of the excitation parameters of the second
electromagnet (8) as a function of the mean value of the
disturbance force (F.sub.d) acting during the stage of
de-excitation of the first electromagnet (8).
2. A method as claimed in claim 1, in which, on the basis of the
mean value of the disturbance force (F.sub.d) acting on the valve
(2) during the de-excitation stage of the first electromagnet (8),
the value of the disturbance force (F.sub.d) is estimated up to the
excitation of the second electromagnet (8).
3. A method as claimed in claim 2, in which it is assumed that the
disturbance force (F.sub.d) has a linear course decreasing from the
estimated mean value to the value respectively between the instant
in which the first electromagnet (8) is substantially cut off and
the instant in which the actuator body (4) comes into abutment
against the second electromagnet (8).
4. A method as claimed in claim 2, in which the excitation
parameters of the second electromagnet (8) are calculated in order
to provide the actuator body (4) with the mechanical energy that it
lacks in order to reach the position of abutment against the second
electromagnet (8) with a substantially zero speed of impact (v),
i.e. to provide the actuator body (4) with the energy dissipated
during the displacement between the position of abutment against
the first upper electromagnet (8) and the position of abutment
against the second electromagnet 8).
5. A method as claimed in claim 4, in which the excitation
parameters of the second electromagnet (8) are calculated by
assuming that the work performed by the second electromagnet (8)
offsets the work (L.sub.d) performed by the disturbance force
(F.sub.d) according to the following equation: 11 L d = X O N X cos
t F m ( x , 2 ( x ) ) + X cos t X 2 F m ( x , 2 ) in which: L.sub.d
is the work performed by the disturbance force (F.sub.d); F.sub.m
is the force generated by the second electromagnet (8); .alpha. is
a control parameter; x is the position of the actuator body (4);
.sub.2 is the magnetic flux of the second electromagnet (8);
.phi..sub.2 is the constant value of magnetic flux with which the
second electromagnet (8) normally operates; X.sub.on is the
position of the actuator body (4), at which the second
electromagnet (8) is activated; X.sub.2 is the final position of
the actuator body (4), at which the actuator body (4) is in
abutment against the second electromagnet (8); X.sub.cost is the
position of the actuator body (4), at which the lower electromagnet
(8) reaches and maintains the magnetic flux value .phi..sub.2.
6. A method as claimed in claim 5, in which the control parameter
(.quadrature.) is calculated by assuming that the actuator body (4)
impacts against the second electromagnet (8) at a desired speed
(V.sub.f) such that the sum of the works of the forces acting on
the actuator body (4) is equal to the kinetic energy possessed by
the oscillating body (4).
7. A method as claimed in claim 2, in which a mechanical energy
(E.sub.M) dynamically stored in the mechanical system (SM) formed
by the actuator body (4) and the elastic body (9) is estimated as a
function of the disturbance force (F.sub.d) and the excitation
parameters of the second electromagnet (8) are calculated as a
function of the difference between an elastic energy (E.sub.E)
statically stored by the elastic body (9) in the abutment position
and the mechanical energy (E.sub.M) dynamically stored in the
mechanical system (SM).
8. A method as claimed in claim 7, in which, as a function of the
disturbance force (F.sub.d), a law of displacement of the actuator
body (4) during the stage between the de-excitation of the first
electromagnet (8) and the excitation of the second electromagnet
(8) is estimated, and the mechanical energy (E.sub.M) dynamically
stored in the mechanical system (SM) is estimated as a function of
the law of displacement of the actuator body (4).
9. A method as claimed in claim 8, in which the law of displacement
is estimated by means of a mathematical model of the mechanical
system, which mathematical model makes provision for the action of
the disturbance force (F.sub.d).
10. A method as claimed in claim 9, in which the mathematical model
makes provision for the action of a viscous friction acting on the
actuator body (4).
11. A method as claimed in claim 10, in which the mathematical
model is defined by the following
equation:m*dv(t)/dt=k*(x(t)-x.sub.0)-F.sub.d(t)-- F.sub.b(t)in
which: m is the mass of the actuator body (4); v(t) is the speed of
the actuator body (4); x(t) is the position of the actuator body
(4); k is the elastic constant of the elastic body (9); x.sub.0 is
the position of the actuator body (4) corresponding to the rest
position of the elastic body (9); F.sub.d(t) is the disturbance
force; F.sub.b(t) is the force of viscous friction.
12. A method as claimed in claim 1, in which the excitation
parameters of each electromagnet (8) comprise the value of the
intensity, the value of the duration and the instant of
commencement of the excitation current (i) which is supplied to the
electromagnet (8).
13. A method as claimed in claim 1, in which the mean value of the
disturbance force (F.sub.d) is calculated during a predetermined
estimation time interval of the stage of de-excitation of the first
electromagnet (8).
14. A method as claimed in claim 13, in which a magnetic flux ()
generated by the first electromagnet (8) is kept constant at an
estimated value (.PHI..sub.S) calculated during the estimation time
interval, this estimated value (.PHI..sub.S) being lower than a
value (.PHI..sub.R) which causes the detachment of the actuator
body (4) from the first electromagnet (8).
15. A method as claimed in claim 14, in which the magnetic flux ()
generated by the first electromagnet (8) is rapidly decreased to
the estimated value (.PHI..sub.S), is kept constant and equal to
the estimated value (.PHI..sub.S) for the estimation time interval
and is lastly rapidly decreased to a zero value.
16. A method as claimed in claim 13, in which the mean value of the
disturbance force (F.sub.d) is calculated by dividing the work
(L.sub.d) performed by the disturbance force during a predetermined
period of time by the displacement performed by the actuator body
(4) during this same period of time.
17. A method as claimed in claim 13, in which the mean value of the
disturbance force (F.sub.d) is calculated by determining the mean
of a series of instantaneous values of the disturbance force
(F.sub.d), each instantaneous value of the disturbance force
(F.sub.d) being determined by dividing the work (L.sub.d) performed
by the disturbance force during a predetermined time interval by
the displacement performed by the actuator body (4) in the same
time interval.
18. A method as claimed in claim 16, in which the work (L.sub.d)
performed by the disturbance force (F.sub.d) during a predetermined
time interval in which the actuator body (4) moves from an initial
to a final position is calculated by applying the following
equation: 12 L d = E E - E K - L m - L v = = 1 2 k ( x f 2 - x i 2
) - 1 2 m ( v f 2 - v i 2 ) - x i x f F m ( x ) x - x i x f F b ( x
) x in which: L.sub.d is the work performed by the disturbance
force; E.sub.E is the elastic energy stored by the elastic body
(9); E.sub.k is the kinetic energy possessed by the actuator body
(4); L.sub.m is the value achieved by the electromagnetic force
generated by the first electromagnet (8); L.sub.v is the work
performed by the force of viscous friction; m is the mass of the
actuator body (4); k is the elastic constant of the elastic body
(9); x is the instantaneous position of the actuator body (4);
x.sub.i is the initial position of the actuator body (4); x.sub.f
is the final position of the actuator body (4); v is the
instantaneous speed of the actuator body (4); v.sub.i is the
initial speed of the actuator body (4); v.sub.f is the final speed
of the actuator body (4); F.sub.m is the electromagnetic force
generated by the first electromagnet (8); F.sub.b is the force of
viscous friction.
19. A method as claimed in claim 18, in which the force of viscous
friction is calculated as the product of the instantaneous speed of
the actuator body (4) and a constant coefficient of viscous
friction.
20. A method as claimed in claim 18, in which the electromagnetic
force is calculated by means of the following equation: 13 F m ( ,
x ) = 1 2 s 2 R 0 ( x ( t ) ) x in which: F.sub.m is the
electromagnetic force; .PHI..sub.S is the estimated value of the
magnetic flux; R.sub.0 is the air gap reluctance of the magnetic
circuit associated with the first electromagnet (8); x is the
instantaneous position of the actuator body (4).
21. A control method for an electromagnetic actuator (1) for the
control of a valve (2) of an engine from an abutment condition, in
which abutment condition an actuator body (4) actuating the valve
(2) and disposed to move between two electromagnets (8) is kept in
abutment against a first excited electromagnet (8) and against the
action of at least one elastic body (9); in order to bring the
actuator body (4) into abutment against a second electromagnet (8),
the first electromagnet (8) is de-excited and the second
electromagnet (8) is subsequently excited, the method being
characterised by the measurement of a mean value of the disturbance
force (F.sub.d) acting on the valve (2) during a predetermined
estimation time interval of the stage of de-excitation of the first
electromagnet (8), a magnetic flux () generated by the first
electromagnet (8) being kept constant at an estimated value
(.PHI..sub.S) determined during the estimation time interval, the
estimated value (.PHI..sub.S) being lower than the value
(.PHI..sub.R) that causes the detachment of the actuator body (4)
from the first electromagnet (8).
22. A method as claimed in claim 21, in which the magnetic flux ()
generated by the first electromagnet (8) is rapidly decreased to
the estimation value (.PHI..sub.S), is kept constant and equal to
the estimation value for the estimation time interval and is lastly
rapidly decreased to a zero value.
23. A method as claimed in claim 21, in which the mean value of the
disturbance force (F.sub.d) is calculated by dividing the work
(L.sub.d) performed by the disturbance force (F.sub.d) during a
predetermined interval of time by the displacement performed by the
actuator body (4) in the same interval of time.
24. A method as claimed in claim 21, in which the mean value of the
disturbance force (F.sub.d) is calculated by determining the mean
of a series of instantaneous values of the disturbance force
(F.sub.d); each instantaneous value of the disturbance force
(F.sub.d) is calculated by dividing the work (L.sub.d) performed by
the disturbance force (F.sub.d) during a predetermined time
interval by the displacement performed by the actuator body (4) in
the same time interval.
25. A method as claimed in claim 23, in which the work (L.sub.d)
performed by the disturbance force (F.sub.d) during a predetermined
time interval in which the actuator body (4) moves from an initial
to a final position is determined by applying the following
equation: 14 L d = E E - E K - L m - L v = = 1 2 k ( x f 2 - x i 2
) - 1 2 m ( v f 2 - v i 2 ) - x i x f F m ( x ) x - x i x f F b ( x
) x in which: L.sub.d is the work performed by the disturbance
force; E.sub.E is the elastic energy stored by the elastic body
(9); E.sub.k is the kinetic energy possessed by the actuator body
(4); L.sub.m is the value achieved by the electromagnetic force
generated by the first electromagnet (8); L.sub.v is the work
performed by the force of viscous friction; m is the mass of the
actuator body (4); k is the elastic constant of the elastic body
(9); x is the instantaneous position of the actuator body (4);
x.sub.i is the initial position of the actuator body (4); x.sub.f
is the final position of the actuator body (4); v is the
instantaneous speed of the actuator body (4); v.sub.i is the
initial speed of the actuator body (4); v.sub.f is the final speed
of the actuator body (4); F.sub.m is the electromagnetic force
generated by the first electromagnet (8); F.sub.b is the force of
viscous friction.
26. A method as claimed in claim 25, in which the force of viscous
friction is calculated as the product of the instantaneous speed of
the actuator body (4) and a constant coefficient of viscous
friction.
27. A method as claimed in claim 25, in which the electromagnetic
force is calculated by means of the following equation: 15 F m ( ,
x ) = 1 2 s 2 R 0 ( x ( t ) ) x in which: F.sub.m is the
electromagnetic force; .PHI..sub.S is the estimated value of the
magnetic flux; R.sub.0 is the air gap reluctance of the magnetic
circuit associated with the first electromagnet (8); x is the
instantaneous position of the actuator body (4).
Description
[0001] The present invention relates to a control method for an
electromagnetic actuator for the control of a valve of an
engine.
BACKGROUND OF THE INVENTION
[0002] As is known, internal combustion engines of the type
disclosed in Italian Patent Application BO99A000443 filed on August
4, 1999, are currently being tested, in which the intake and
exhaust valves are moved by electromagnetic actuators. These
electromagnetic actuators have undoubted advantages, as they make
it possible to control each valve according to a law optimised for
any operating condition of the engine, while conventional
mechanical actuators (typically camshafts) make it necessary to
define a lift profile for the valves which represents an acceptable
compromise for all the possible operating conditions of the
engine.
[0003] An electromagnetic actuator for a valve of an internal
combustion engine of the type described above normally comprises an
actuator body, which is connected to the stem of the valve and, in
rest conditions, is held by at least one spring in an intermediate
position between two de-excited electromagnets; in operation, the
electromagnets are controlled so as alternately to exert a force of
attraction of magnetic origin on the actuator body in order to
displace this actuator body between the two limit abutment
positions, which correspond to a position of maximum opening and a
position of closure of the respective valve.
[0004] In order to displace the valve from the position of maximum
opening to the closed position or vice versa, the actuator body has
to be displaced from a position of abutment against a first
electromagnet to a position of abutment against a second
electromagnet; for the purposes of performing this displacement,
the first electromagnet is de-excited and the second electromagnet
is subsequently excited with the excitation parameters, i.e. with
values of intensity, duration and instant of commencement of the
excitation current, depending on the engine point.
[0005] It has been observed, however, that in the known
electromagnetic actuators of the type described above, the position
of abutment against the second electromagnet is normally reached
with a relatively high speed of impact of the actuator body against
the second electromagnet, which causes both substantial mechanical
stresses on the electromagnetic actuator and a high level of noise
generated by the electromagnetic actuator.
[0006] In order to attempt to remedy the above-described drawbacks,
it has been proposed to use an external position sensor, which
provides, instant by instant, the exact position of the actuator
body and makes it possible precisely to control the actual position
of the actuator body; position sensors able to provide the
precision and service life needed for profitable use for this
purpose are not, however, commercially available.
SUMMARY OF THE INVENTION
[0007] The object of the present invention is to provide a control
method for an electromagnetic actuator for the control of a valve
of an engine, which is free from the above-mentioned drawbacks and,
in particular, is easy and economic to embody.
[0008] The present invention therefore relates to a control method
for an electromagnetic actuator for the control of a valve of an
engine as claimed in claim 1.
BRIEF DESCRIPTION OF THE DRAWINGS
[0009] The present invention will be described below with reference
to the accompanying drawings, which show a non-limiting embodiment
thereof, in which:
[0010] FIG. 1 is a diagrammatic view, in lateral elevation and
partial cross-section, of a valve of an engine and a relative
electromagnetic actuator operating according to the method of the
present invention;
[0011] FIG. 2 is a diagram of an electromagnetic circuit of the
actuator of FIG. 1;
[0012] FIG. 3 shows graphs of the time curve of some magnitudes
characteristic of the electromagnetic actuator of FIG. 1.
DETAILED DESCRIPTION OF THE INVENTION
[0013] In FIG. 1, an electromagnetic actuator (of the type
disclosed in European Patent Application EP1087110) is shown
overall by 1 and is coupled to an intake or exhaust valve 2 of an
internal combustion engine of known type in order to displace the
valve 2 along a longitudinal axis 3 of the valve between a closed
position (known and not shown) and a position of maximum opening
(known and not shown).
[0014] The electromagnetic actuator 1 comprises an oscillating arm
4 made at least partly from ferromagnetic material, which has a
first end hinged on a support 5 so as to be able to oscillate about
an axis of rotation 6 transverse to the longitudinal axis 3 of the
valve 2, and a second end connected by a hinge 7 to an upper end of
the valve 2. The electromagnetic actuator 1 further comprises two
electromagnets 8 borne in a fixed position by the support 5 so that
they are disposed on opposite sides of the oscillating arm 4, and a
spring 9 coupled to the valve 2 and adapted to maintain the
oscillating arm 4 in an intermediate position (shown in FIG. 1) in
which this oscillating arm 4 is equidistant from the polar
expansions 10 of the two electromagnets 8. According to a different
embodiment which is not shown, the spring 9 coupled to the valve 2
is flanked by a torsion bar spring coupled to the hinge disposed
between the support 5 and the oscillating arm 4.
[0015] In operation, a control unit 11 controls the position of the
oscillating arm 4, i.e. the position of the valve 2, in feedback
and in a substantially known manner, on the basis of the engine
operating conditions; the control unit 11 in particular excites the
electromagnets 8 in order alternately or simultaneously to exert a
force of attraction of magnetic origin on the oscillating arm 4 in
order to cause it to rotate about the axis of rotation 6 thereby
displacing the valve 2 along the respective longitudinal axis 3 and
between the above-mentioned positions of maximum opening and
closure (not shown).
[0016] As shown in FIG. 1, the valve 2 is in the above-mentioned
closed position (not shown) when the oscillating arm 4 is in
abutment on the excited upper electromagnet 8, is in the
above-mentioned position of maximum opening (not shown) when the
oscillating arm 4 is in abutment on the excited lower electromagnet
8, and is in a partially open position when both electromagnets are
de-excited and the oscillating arm 4 is in the above-mentioned
intermediate position (shown in FIG. 1) as a result of the force
exerted by the spring 9.
[0017] As shown in FIG. 2, each electromagnet 8 comprises a
respective magnetic core 12 coupled to a corresponding coil 13,
which is supplied by the control unit 11 with a current i(t) that
is variable over time in order to generate a flux (t) via a
respective magnetic circuit 14 coupled to the coil 13. Each
magnetic circuit 14 is in particular formed by the relative core 12
of ferromagnetic material, the oscillating arm 4 of ferromagnetic
material and the air gap 15 between the relative core 12 and the
oscillating arm 4.
[0018] Each magnetic circuit 14 has an overall reluctance R defined
by the sum of the reluctance of the iron R.sub.fe and the
reluctance of the air gap R.sub.0 (equation [2]); the value of the
flux (t) circulating in the magnetic circuit 14 is linked to the
value of the current i(t) circulating in the relative coil 13 by
equation [1], in which N is the number of turns of the coil 13:
N*i(t)=R*(t) [1]
R=R.sub.fe+R.sub.0 [2]
[0019] In general, the value of the overall reluctance R depends
both on the position x(t) of the oscillating arm 4 (i.e. on the
amplitude of the air gap 15, which is equal, less a constant, to
the position x(t) of the oscillating arm 4), and on the value
assumed by the flux (t). Leaving aside negligible errors, i.e. as a
first approximation, it can be considered that the reluctance value
of the iron R.sub.fe depends only on the value assumed by the flux
(t), while the value of the reluctance of the air gap R.sub.0
depends only on the position x(t), i.e.:
R(x(t), (t))=R.sub.fe((t))+R.sub.0(x(t)) [3]
N*i(t)=R(x(t), (t))*(t) [4]
N*i(t)=R.sub.fe((t))*(t)+R.sub.0(x(t))*(t) [5]
N*i(t)=H.sub.fe((t))+R.sub.0(x(t))*(t) [6]
R.sub.0(x(t))=(N*i(t)-H.sub.fe( (t)))/(t) [7]
[0020] It is then clear from equation [7] that it is possible to
calculate the value assumed by the reluctance of the air gap
R.sub.0, and therefore the position x(t) of the oscillating arm 4,
when the value assumed by the flux (t) and the value assumed by the
current i(t) are known; in particular, once the value assumed by
the reluctance of the air gap R.sub.0 has been calculated, it is
relatively simple to obtain the position x(t) of the oscillating
arm 4 as the structural properties of the magnetic circuits 14 are
known.
[0021] The relationship between the air gap reluctance R.sub.0 and
the position x can be obtained relatively simply by analysing the
characteristics of the magnetic circuit 14 (an example of a
behavioural model of the air gap 15 is shown in equation [9]
below). Once the relationship between the air gap reluctance
R.sub.0 and the position x is known, the position x can be obtained
from the air gap reluctance R.sub.0 by applying the inverse
relationship (applicable using either the exact equation, or by
using an approximate method of digital calculation). The following
equations summarise the above: 1 R o ( x ( t ) ) = N i ( t ) - H fe
( ( t ) ) ( t ) [ 8 ]
R.sub.0(x(t))=K.sub.1[1-e.sup.-k.sup..sub.2.sup..multidot.x(t)+k.s-
ub.3.multidot.x(t)]+K.sub.0 [9]
[0022] 2 x ( t ) = R 0 - 1 ( R o ( x ( t ) ) ) = R 0 - 1 ( N i ( t
) - H fe ( ( t ) ) ( t ) ) [ 10 ]
[0023] The constants K.sub.0, K.sub.1, K.sub.2, K.sub.3 are
constants that can be obtained experimentally by means of a series
of measurements of the magnetic circuit 14.
[0024] It will be appreciated from the above that the position x(t)
of the oscillating arm 4 may be precisely calculated only when the
value assumed by the flux (t) is significantly non-zero, i.e. when
at least one of the electromagnets 8 is excited; when both the
electromagnets 8 are de-excited, it is not possible to calculate
the position x(t) of the oscillating arm 4.
[0025] As shown in FIG. 3, at the time instant to the upper
electromagnet 8 is excited, the lower electromagnet 8 is
de-excited, and the oscillating arm 4 is immobile in a position of
abutment against the upper electromagnet 8, which abutment position
conventionally corresponds to a value X.sub.1 of the position x(t)
of the oscillating arm 4; the above-mentioned intermediate rest
position corresponds to a zero value of the position x(t) of the
oscillating arm 4, and the position of abutment against the lower
electromagnet 8 corresponds to a value X.sub.2 of the position x(t)
of the oscillating arm 4. In order to displace the oscillating arm
4 from the position of abutment against the upper electromagnet 8
to the position of abutment against the lower electromagnet 8, i.e.
in order to bring the valve 2 from the closed position to the
position of maximum opening, the upper electromagnet 8 is
de-excited and the lower electromagnet 8 is subsequently
excited.
[0026] From the time instant t.sub.0, the upper electromagnet 8 is
partially de-excited by the control unit 11 by varying the
excitation current i(t) supplied to the upper electromagnet 8, so
as rapidly to reduce the magnetic flux (t) generated by the upper
electromagnet 8 from an operating value .PHI..sub.1 to an estimated
value .PHI..sub.s, to maintain the flux (t) at the estimated value
.PHI..sub.S for an estimation time interval (included between the
time instants t.sub.2 e t.sub.3), and lastly rapidly to zero-set
the flux (t). The estimated value .PHI..sub.S is lower than the
value .PHI..sub.R which causes the oscillating arm 4 to be detached
from the upper electromagnet 8; for this reason, from the time
instant t.sub.1, in which the flux (t) becomes lower than the value
.PHI..sub.R the oscillating arm 4 is detached from the upper
electromagnet 8 and starts to move towards the lower electromagnet
8 as a result of the elastic force exerted by the spring 9.
[0027] During the estimation time interval, the control unit 11
estimates the mean value of the disturbance force F.sub.d acting on
the valve 2 as a result of the action of the gases in the cylinder
(not shown); in particular, the instantaneous value of the
disturbance force F.sub.d at a sequence of N time intervals
included in the estimation time interval (i.e. between the time
instants t.sub.2 e t.sub.3) is estimated and the mean of the N
instantaneous values is calculated by applying equation [11]: 3 F d
m e d i a = 1 N k = 1 N F d k [ 11 ]
[0028] In order to estimate the instantaneous value of the
disturbance force F.sub.d at a kth instant in which the oscillating
arm 4 is in the position x.sub.k, equation [12], in which L.sub.d
is the work performed by the disturbance force F.sub.d, is applied:
4 F d k = L d x = L d k - L d k - 1 x d k - x d k - 1 [ 12 ]
[0029] The work L.sub.d performed by the disturbance force F.sub.d
during a predetermined time interval in which the oscillating arm 4
moves from an initial to a final position is calculated by applying
equation [13]: 5 L d = E E - E K - L m - L v = = 1 2 k ( x f 2 - x
i 2 ) - 1 2 m ( v f 2 - v i 2 ) - x i x f F m ( x ) x - x i x f F b
( x ) x [ 13 ]
[0030] in which:
[0031] L.sub.d is the work performed by the disturbance force
F.sub.d;
[0032] E.sub.E is the elastic energy stored by the spring 9;
[0033] E.sub.k is the kinetic energy possessed by the oscillating
arm 4;
[0034] L.sub.m is the value achieved by the electromagnetic force
generated by the upper electromagnet 8;
[0035] L.sub.v is the work performed by the force of viscous
friction;
[0036] m is the mass of the oscillating arm 4;
[0037] k is the elastic constant of the spring 9;
[0038] x is the instantaneous position of the oscillating arm
4;
[0039] X.sub.i is the initial position of the oscillating arm
4;
[0040] X.sub.f is the final position of the oscillating arm 4;
[0041] v is the instantaneous speed of the oscillating arm 4;
[0042] v.sub.i is the initial speed of the oscillating arm 4;
[0043] v.sub.f is the final speed of the oscillating arm 4;
[0044] F.sub.m is the electromagnetic force generated by the upper
electromagnet 8;
[0045] F.sub.b is the force of viscous friction acting on the
oscillating arm 4.
[0046] In particular, the value of the force of viscous friction
F.sub.b acting on the oscillating arm 4 is calculated as the
product of the instantaneous speed v(t) of the oscillating arm 4
and a coefficient of viscous friction which is constant or depends
on temperature. During the estimation time interval, the value of
the flux (t) is constant and equal to the estimation value
.PHI..sub.S; during the estimation time interval, therefore, the
electromagnetic force F.sub.m generated by the upper electromagnet
8 is calculated by equation [14]: 6 F m ( , x ) = - 1 2 R ( x ( t )
, ( t ) ) x 2 ( t ) = = 1 2 s 2 R 0 ( x ( t ) ) x [ 14 ]
[0047] It will be appreciated that the value of the position x(t)
of the oscillating arm 4 during the estimation time interval is
calculated by applying equation [10], while the value of the speed
v(t) of the oscillating arm 4 during the estimation time interval
is calculated by deriving the value of the position x(t) over
time.
[0048] At the end of the estimation time interval, the upper
electromagnet 8 is de-excited and, until the lower electromagnet 8
is activated, the control unit 11 manages to calculate the value of
the position x(t) of the oscillating arm 4 by applying the equation
[10]; moreover, the control unit 11 also has to know the
development over time of the position x(t) of the oscillating arm 4
after the de-excitation of the upper electromagnet 8 in order
accurately to determine the excitation parameters of the lower
electromagnet 8 (intensity, duration and instant of commencement of
the relative excitation current i(t)) in order to cause the
oscillating arm 4 to impact against the lower electromagnet 8 at a
substantially zero speed.
[0049] In order also to estimate the development over time of the
position x(t) of the oscillating arm 4 after the de-excitation of
the upper electromagnet 8, the control unit 11 uses a mathematical
model of the mechanical system SM comprising the oscillating arm 4
and the spring 9, which mathematical model is summarised by
equation [15]:
m*dv(t)/dt=k*(x(t)-X.sub.0)-F.sub.d(t)-F.sub.b(t) [15]
[0050] in which:
[0051] m is the mass of the oscillating arm 4;
[0052] v(t) is the speed of the oscillating arm 4;
[0053] x(t) is the position of the oscillating arm 4;
[0054] k is the elastic constant of the spring 9;
[0055] X.sub.0 is the position of the oscillating arm 4
corresponding to the rest position of the spring 9;
[0056] F.sub.d(t) is the disturbance force;
[0057] F.sub.b(t) is the force of viscous friction.
[0058] In order to apply equation [15], the control unit 11 has to
estimate the instantaneous value of the disturbance force F.sub.d
acting on the valve 2 from the de-excitation excitation of the
upper electromagnet 8 up to the excitation of the lower
electromagnet 8 using the mean value of the disturbance force
F.sub.d calculated during the estimation time interval; in
particular, the control unit 11 assumes that the disturbance force
F.sub.d has a linear course decreasing from the estimated mean
value to the zero value respectively between the instant in which
the upper electromagnet 8 is substantially cut off and the instant
in which the oscillating arm 4 comes into abutment against the
lower electromagnet 8.
[0059] The above-mentioned excitation parameters of the lower
electromagnet 8 are calculated so as to supply the oscillating arm
4 with the mechanical energy that it lacks in order to reach the
desired abutment position with a substantially zero speed of impact
v(t), i.e. to provide the oscillating arm 4 with the energy
dissipated during the displacement between the position of abutment
against the upper electromagnet 8 and the position of abutment
against the lower electromagnet 8.
[0060] In particular, the excitation parameters of the lower
electromagnet 8 are calculated as a function of the estimate of the
mean disturbance force F.sub.dmedia obtained by equation [11]; as
the initial value of the mean disturbance force F.sub.dmedia is
known and the model of development of the disturbance force F.sub.d
is defined (as mentioned above, the control unit 11 assumes that
the disturbance force F.sub.d has a linear course decreasing from
the estimated mean value to the zero value respectively between the
instant in which the upper electromagnet 8 is substantially cut off
and the instant in which the oscillating arm 4 comes into abutment
against the lower electromagnet 8), the work L.sub.d performed by
the disturbance force F.sub.d can be readily obtained from equation
[16] (in which X.sub.i is the initial position and X.sub.f is the
final position of action of the disturbance force F.sub.d): 7 L d =
X i X f F d ( x ) x [ 16 ]
[0061] Assuming that the work performed by the lower electromagnet
8 offsets the work L.sub.d performed by the disturbance force
F.sub.d provides equation [17]: 8 L d = X O N X cos t F m ( x , 2 (
x ) ) + X cos t X 2 F m ( x , 2 ) [ 17 ]
[0062] in which:
[0063] F.sub.m is the force generated by the lower electromagnet 8
(see, for reference, equation [14]);
[0064] .alpha. is a control parameter;
[0065] .phi..sub.2 is the constant value of magnetic flux .sub.2
with which the lower electromagnet 8 normally operates;
[0066] X.sub.on is the position of the oscillating arm 4, at which
the lower electromagnet 8 is activated;
[0067] X.sub.2 is the final position of the oscillating arm 4, at
which the oscillating arm 4 is in abutment against the lower
electromagnet 8;
[0068] X.sub.cost is the position of the oscillating arm 4, at
which the lower electromagnet 8 reaches and maintains the magnetic
flux value .phi..sub.2.
[0069] Resolving equation [17] makes it possible to obtain the
values of the parameters X.sub.on and .phi..sub.2 which
characterise the excitation of the lower electromagnet 8.
[0070] The control parameter a is needed to optimise the successive
phase of closed loop control of the lower electromagnet 8, so that
when the oscillating arm 4 reaches the position of abutment against
the lower electromagnet 8, the energy equilibrium defined by
equation [18] (in which m is the mass of the oscillating arm 4 and
L.sub.i are the works of the forces acting on the oscillating arm
4) occurs, i.e. the oscillating arm 4 impacts on the lower
electromagnet 8 with a desired speed V.sub.f: 9 i L i = 1 2 m V f 2
[ 18 ]
[0071] According to a further embodiment, the excitation parameters
of the lower electromagnet 8 are calculated as a function of the
difference existing between an elastic energy E.sub.E statically
stored by the spring 9 in the position of abutment against the
lower electromagnet 8 (i.e. in the desired position) and the
mechanical energy E.sub.M dynamically stored in the mechanical
system SM; this mechanical energy E.sub.M is calculated by applying
equation [19] and using the values of the position x(t) and the
speed v(t) of the oscillating arm 4 provided by the resolution of
equation [15]: 10 E M ( t ) = E E ( t ) + E K ( t ) = 1 2 k ( x 2 (
t ) - X 0 2 ) + 1 2 m v 2 ( t ) [ 19 ]
[0072] in which:
[0073] m is the mass of the oscillating arm 4;
[0074] v(t) is the speed of the oscillating arm 4;
[0075] k is the elastic constant of the spring 9;
[0076] X0 is the position of the oscillating arm 4 corresponding to
the rest position of the spring 9.
[0077] Obviously, when the lower electromagnet 8 is excited and in
stable operation (i.e. at the end of an activation transient) it is
possible to precisely to calculate, by applying equation [10], the
position x(t) of the oscillating arm 4 and, therefore, to control
in feedback the position x(t) and the speed v(t) of the oscillating
arm 4 in order to try to obtain a substantially zero speed of
impact against the lower electromagnet 8; however, the
possibilities of final correction by means of the feedback control
are relatively modest and, in order to be really efficient, have to
be combined with the previous control of the excitation of the
lower electromagnet 8 described above.
* * * * *